The width of a rectangle with a length of 72 is 90 inches.
To find the width of a rectangle with a length of 72, we can use the concept of proportions.
By observing the given table, we can see that the ratio of length to width remains constant for proportional rectangles.
Let's calculate the common ratio:
[tex]\( \text{Ratio} = \frac{\text{Length}}{\text{Width}} = \frac{8}{10} = \frac{12}{15} = \frac{24}{30} = \frac{32}{40} \)[/tex]
Now, we can set up a proportion to find the width for a length of 72:
[tex]\( \frac{72}{\text{Width}} = \frac{8}{10} \)[/tex]
Cross-multiplying, we have:
[tex]\( 72 \times 10 = 8 \times \text{Width} \)[/tex]
Simplifying, we get:
[tex]\( 720 = 8 \times \text{Width} \)[/tex]
Dividing both sides by 8, we find:
[tex]\( \text{Width} = \frac{720}{8} = 90 \)[/tex]
Therefore, the width of a rectangle with a length of 72 is 90 inches.
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The table below could be a mathematical model for some situation.
X -8-6-3-1 1
y-22-18-10 -7 -4
What is the average rate of change over the interval from -3 to 1?
(Round to three decimal places)
The average rate of change over the interval from -3 to 1 is 2.000
How to find the average rate of changeTo find the average rate of change over the interval from -3 to 1, we need to calculate the change in y divided by the change in x.
Δy = y₂ - y₁ = (-10) - (-18) = 8
Δx = x₂ - x₁ = 1 - (-3) = 4
Now, we can calculate the average rate of change using the formula:
Average Rate of Change = Δy / Δx
Average Rate of Change = 8 / 4 = 2
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f(x) = x^2−4x+2, find the value(s) for x such that f(x)=23.
Step-by-step explanation:
To find the value(s) for x such that f(x) = 23, we can set up the equation:
x^2 - 4x + 2 = 23
To solve this quadratic equation, we need to rearrange it into the standard quadratic form:
x^2 - 4x - 21 = 0
Now, we can solve this equation by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation x^2 - 4x - 21 = 0, the coefficients are: a = 1, b = -4, and c = -21.
Plugging these values into the quadratic formula, we get:
x = (-(-4) ± √((-4)^2 - 4(1)(-21))) / (2(1))
x = (4 ± √(16 + 84)) / 2
x = (4 ± √100) / 2
x = (4 ± 10) / 2
Now, we have two solutions:
x = (4 + 10) / 2 = 14 / 2 = 7
x = (4 - 10) / 2 = -6 / 2 = -3
Therefore, the values for x such that f(x) = 23 are x = 7 and x = -3.
The locations of student desks are mapped using a coordinate plane where the origin represents the center of the classroom. Maria's desk is located at (4, −1), and Monique's desk is located at (−4, 3). If each unit represents 1 foot, what is the distance from Maria's desk to Monique's desk?
Answer:
the distance from Maria's desk to Monique's desk is approximately 8.94 feet.
Find the measure of
Answer:
∠ ADE = 55° , ∠ ACE = 32.5° , ∠ BAD = 22.5°
Step-by-step explanation:
the measure of the inscribed angle ADE is half the measure of its intercepted arc AE , then
∠ ADE = [tex]\frac{1}{2}[/tex] × 110° = 55°
---------------------------------
the measure of the secant- secant angle ACE is half the difference of the measures of the intercepted arcs , that is
∠ ACE = [tex]\frac{1}{2}[/tex] (AE - BD) = [tex]\frac{1}{2}[/tex] (110 - 45)° = [tex]\frac{1}{2}[/tex] × 65° = 32.5°
-----------------------------------------
the measure of the inscribed angle BAD is half the measure of its intercepted arc BD , that is
∠ BAD = [tex]\frac{1}{2}[/tex] × 45° = 22.5°
In 1995, wolves were introduced into Yellowstone Park.
The function `w\left(x\right)=14\cdot1.08^{x}` models the number of wolves, `w`, in the years since 1995, `x`.
According to the model, about how many years will it take for the population to reach `500` wolves?
According to the information we can infer that it will take approximately 31 years for the wolf population to reach 500.
How to calculate how many years will it take for the population to reach 500 wolves?The given function, w(x) = 14 * 1.08^x, models the number of wolves (w) in the years since 1995 (x).
To find the number of years it will take for the population to reach 500 wolves, we can set up the equation:
500 = 14 * [tex]1.08^{x}[/tex]Dividing both sides by 14, we get:
35.714 ≈ [tex]1.08^{x}[/tex]Taking the logarithm (base 1.08) of both sides to solve for x:
log₁.₀₈ (35.714) ≈ log₁.₀₈ ([tex]1.08^{x}[/tex])x ≈ log₁.₀₈ (35.714)Using a calculator, we find that x ≈ 31.
According to the above it will take approximately 31 years for the wolf population to reach 500 based on the given model.
Note: This question is incomplete. Here is the complete information:
Attached image
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3) ABCD is a rectangle.
The line that contains BA is y=-x+3. Write the
equations of the lines that contain BC, AD, and CD
The equations of the other line are:
BC: y = 2x
AD: y = 2x + 2
CD = -¹/₂x + 5.5
How to find the equation of the Line?The formula for the equation of a line between two coordinates is expressed as:
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
Thus, for the lines we have:
BC has B(-2, 4) and C(-1, 6)
Thus:
BC: (y - 4)/(x - 2) = (6 - 4)/(-1 + 2)
BC: (y - 4)/(x - 2) =2
BC: y - 4 = 2x - 4
BC: y = 2x
AD has A(2,2) and D(3, 4)
Thus:
AD: (y - 2)/(x - 2) = (4 - 2)/(3 - 2)
AD: y - 2 = 2x - 4
AD: y = 2x + 2
CD has C(-1, 6) and D(3, 4)
CD: (y - 6)/(x + 1) = (4 - 6)/4
CD: y - 6 = -¹/₂(x + 1)
CD = -¹/₂x + 5.5
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how would I solve this?
If sinθ = 5/13 and θ is in Quadrant II, then sin (θ/2) will be equal to [tex]\frac{5}{\sqrt{26}}[/tex]
How to Solve Half-AnglesTo find sin(θ/2), we can use the half-angle identity for sine, which states that:
sin(θ/2) = ±[tex]\sqrt{\frac{(1 - cos\theta)}{2}}[/tex]
Given that sinθ = 5/13 and θ is in Quadrant II, we can determine the value of cosθ using the Pythagorean identity
sin²θ + cos²θ = 1
sinθ = 5/13
sin²θ = (5/13)² = 25/169
cos²θ = 1 - sin²θ = 1 - 25/169 = 144/169
cosθ = ±√(144/169) = ±12/13
Since θ is in Quadrant II, the cosine is negative. Therefore, cosθ = -12/13.
Now, we can calculate sin(θ/2):
sin(θ/2) = ±√((1 - cosθ) / 2) = ±√((1 - (-12/13)) / 2) = ±√((1 + 12/13) / 2) = ±√(25/26) = ±5/√26
Since θ is in Quadrant II, sin(θ/2) will be positive.
Therefore, sin(θ/2) = 5/√26.
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Please look at photo. I’ll give good rating!
An output value for (fog)(x) is 55/(x² + 2x).
Domain = (-∞, 1) U (-2, 0) U (0, ∞) or {x|x ≠ 0, -2}.
How to determine the corresponding composite function?In this exercise, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations in simplified form as follows;
(fog)(x) = 5/(x + 2) × 11/x
(fog)(x) = 55/x(x + 2)
(fog)(x) = 55/(x² + 2x)
For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;
x² + 2x ≠ 0
x² ≠ -2x
x ≠ -2
Domain = (-∞, 1) U (-2, 0) U (0, ∞) or {x|x ≠ 0, -2}.
In conclusion, we can reasonably infer and logically deduce that x must not be equal to 0 and -2.
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-Ready
Algebraic Expressions with Exponents-Instruction-Level F
Amelia is building 3 square garden beds that are all the same size. She arranges them side-
by-side to separate certain plants. Amelia wants to know the total area of the garden beds.
length (ft) of one side of a garden bed
Write an expression to show the total
area of the garden beds.
38²
What is the total area if each garden
bed has a length of 4 feet?
ft²
A = $²
7 8 9
6
3
4
51
1
1 2
X
1
t
X
The correct answer is each garden bed has a length of 4 feet, the total area of the garden beds is 48 square feet.
To find the total area of the garden beds, we can use the expression:
Total area = (length of one side)^2 * number of garden beds
Given that each garden bed has a length of 4 feet, we substitute 4 for the length of one side in the expression:
Total area = (4)^2 * 3
Simplifying:
Total area = 16 * 3
Total area = 48 square feet
Therefore, if each garden bed has a length of 4 feet, the total area of the garden beds is 48 square feet.
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find g[h(-2)] from f(x)=x^(2),g(x)=5x , h(x)=x+4
Explanation:
Plug x = -2 into h(x)
h(x) = x+4
h(-2) = -2+4
h(-2) = 2
This means g[ h(-2) ] = g(2) after replacing h(-2) with 2.
g(x) = 5x
g(2) = 5*2
g(2) = 10
Therefore, g[ h(-2) ] = 10
Calculate continuous growth and decay
Question
In 2010 the Network Club membership was 2,500. With an annual growth rate of approximately 8%, compounded
continuously, what will the membership be in 2020?
Round the answer to the nearest whole number, and do not include the units in your answer.
Provide your answer below:
Reflect in ePortfolio
FEEDBACK
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SUBMIT
E
Rounding to the nearest whole number, the membership of the Network Club in 2020 will be approximately 5,564.
Therefore, the correct answer is: E. 5,564.
To calculate the membership of the Network Club in 2020, we can use the continuous growth formula:
[tex]A = P \times e^{(rt)[/tex]
Where:
A is the final amount or membership in 2020,
P is the initial amount or membership in 2010,
e is the mathematical constant approximately equal to 2.71828,
r is the annual growth rate as a decimal,
t is the number of years.
Given:
P = 2,500 (membership in 2010),
r = 8% = 0.08 (annual growth rate),
t = 2020 - 2010 = 10 years (number of years).
Plugging in the values into the formula, we have:
[tex]A = 2,500 \times e^{(0.08 \times 10)}[/tex]
Calculating the exponent:
[tex]A = 2,500 \times e^{(0.8)[/tex]
Using a calculator, we find that[tex]e^{(0.8)[/tex] is approximately 2.22554.
Now, we can calculate the final amount A:
A ≈ 2,500 [tex]\times[/tex] 2.22554 ≈ 5,563.85
Therefore, the correct answer is: E. 5,564.
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Answer: The answer is 5564
Step-by-step explanation: P=I[tex]e^rt[/tex]=2500e^(0.08)(10)=5563.85
if (2i/2+i) - 3i(3+i) = a + bi then a= ____ and b=_____
A = 1/10, -10, 1/50, -1/10
B = i/10, -10i, -1/10, -1/50
The value of a and b in the given complex expression is 1/10 and -1/10 respectively.
This is a problem related to the complex numbers. The complex numbers has a general form of (a+bi) where 'i' is the imaginary number or √-1. The part without an 'i' is called Real Part and the part with an 'i' is called Imaginary Part.
(2i/2+i) - 3i/(3+i) = a + bi
{ 2i(3+i) - 3i(2+i) }/ (2 + i)(3 + i) = a+bi
6i + 2i² - 6i - 3i² / (2 + i)(3 + i) = a+bi
(-2 + 3) / (6 + 5i - 1) = s+bi
1 / (5 + 5i) = a+bi
Now we multiply top and bottom by 5 - 5i :
5 - 5i / (5 + 5i)(5 - 5i) = a+bi
5 - 5i / 25 -25i² = a+bi
5 - 5i / 50 = a+bi
1/10 - 1/10i = a+bi
On comparing the real and imaginary part on the both sides:
a= 1/10 , b= -1/10.
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Please see my question in the attachment, thanks
As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.
What is a vertical asymptote?In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).
By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.
In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;
As x → -1⁻, f(x) → ∞.
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cual es la definición de un segmento de recta
A line segment is a fundamental concept in geometry, representing a portion of a line that has a definite beginning and end. It consists of an infinite number of points situated between two endpoints.
What are the endpoints of a line segment?The endpoints themselves are distinct points on a line, and they are included as part of the line segment. Unlike a line, which extends indefinitely in both directions, a line segment is confined to a specific length.
This length is often referred to as the 'measure' of the line segment. Additionally, line segments serve as building blocks for various geometrical shapes and figures by connecting multiple points in space.
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The Question in English
What is the definition of a line segment?
The units of measurement for surface area are always cubed.
O False
O True
Answer:
False
Step-by-step explanation:
When calculating volume, units of measurement are cubed. When calculating surface area, units of measurement are squared.
Further explanation:
Let's say you are finding the area of a rectangle. The length is 5in and the width is 7 in.
since you know l*w is area, you need to multiply 5in and 7in. 5*7=35 and then the two units of measurement, in*in=in^2 so 5in*7in=35in^2. the unit is squared not cubed.
The units of measurement for surface area are always SQUARED. Hence the correct answer is FALSE.
In 2-D, the total space covered by any two-dimensional figure is called Area while if we talk about 3-D, the total area of all the outer surfaces when added, sums up to form the Surface Area. Hence, the surface area is the multiplication of any two of the physical quantities.
For example,
Area of a square=(side x side)
=(metre x metre) or (cm x cm) [in terms of units]
= [tex]metre^{2}[/tex] or [tex]cm^{2}[/tex]
Similarly,
Surface Area of cube=6x(side x side) [summation of the area of 6 faces of cube]
=(metre x metre) or (cm x cm) [in terms of units]
= [tex]metre^{2}[/tex] or [tex]cm^{2}[/tex] (again)
Therefore, The units of measurement for the surface area are always SQUARED. Hence the correct answer is FALSE.
When talking of volume, since volume is the amount of space taken by any object or any 3-Dimensional body, the units of measurement of Volume are always cubed. For example, [tex]metre^{3}[/tex] or [tex]cm^{3}[/tex].
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Is the relation shown in the table below a function? (type in yes or no)
Answer:
Yes
Step-by-step explanation:
To know if a table is a function or not, we have to see if 1 input only has 1 output.
Looking at the table each input only has 1 output, so it is a function.
The value v of a tractor purchased for $13,000 and depreciated linearly at the rate of $1,300 per year is given by v= -1,300t+13,000, where t represents the number of years since the
purchase. Find the value of the tractor after (a) two years and (b) six years. When will the tractor have no value?
a) the value of the tractor after two years is $10,400.
b) the value of the tractor after six years is $5,200.
To find the value of the tractor after a certain number of years, we can substitute the value of t into the equation v = -1,300t + 13,000.
a) After two years:
Substituting t = 2 into the equation, we get:
v = -1,300(2) + 13,000
v = -2,600 + 13,000
v = 10,400
Therefore, the value of the tractor after two years is $10,400.
b) After six years:
Substituting t = 6 into the equation, we get:
v = -1,300(6) + 13,000
v = -7,800 + 13,000
v = 5,200
Therefore, the value of the tractor after six years is $5,200.
To find when the tractor will have no value, we need to find the value of t when v = 0. We can set the equation v = -1,300t + 13,000 equal to 0 and solve for t:
-1,300t + 13,000 = 0
-1,300t = -13,000
t = -13,000 / -1,300
t = 10
Therefore, the tractor will have no value after 10 years.
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Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x) and express P(x) in the form dix) Q(x) R(x).
P(x)=x^3+3x²-8x+140
d(x)=x+7
P(x) = (x+7)( ) +
The polynomial P(x) = x³ + 3x² - 8x + 140 divided by (x + 7), will give a quotient of x² - 3x + 2 and a remainder of 0 using the long division, we can write P(x) = (x + 7)(x² - 4x + 20) + 0
What is a polynomialA polynomial is a mathematical expression which have a sum of powers in one or more variables with coefficients. The highest power of the variable in a polynomial is called its degree.
We shall divide the polynomial x³ + 3x² - 8x + 140 by x + 7 as follows;
x³ divided by x equals x²
x + 7 multiplied by x² equals x³ + 7x²
subtract x³ - x² from x³ + 3x² - 8x + 140 will result to -4x² - 8x + 140
-4x² divided by x equals -4x
x + 7 multiplied by -4x equals -4x² - 28x
subtract -4x² - 28x from -4x² - 8x + 140 will result to 20x + 140
20x divided by x equals 20
x + 7 multiplied by 20 equals 20x + 140
subtract 20x + 140 from 20x + 140 will result to a remainder 0
Therefore, the polynomial P(x) = x³ + 3x² - 8x + 140 divided by (x + 7), will give a quotient of x² - 3x + 2 and a remainder of 0 using the long division, we can write P(x) = (x + 7)(x² - 4x + 20) + 0
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3
2
1
-1
-2
-3
Determine the period.
2
4
6
8
10 12 14
The calculated period of the function is 12
How to determine the period of the functionFrom the question, we have the following parameters that can be used in our computation:
The graph
By definition, the period of the function is calculated as
Period = Difference between cycles or the length of one complete cycle
Using the above as a guide, we have the following:
Period = 13 - 1
Evaluate
Period = 12
Hence, the period of the function is 12
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A file that is 268 megabytes is being downloaded if the download is 14.3% complete how many megabytes have been downloaded
Please show the graph with correct points in x and y. Please specify if it’s a hollow dot or solid dot for each point. I’ll give good rating! Thank you!
The solution to the piecewise-defined function is shown in the attached graph.
Understanding Piecewise FunctionThe function g(x) is defined as follows:
g(x) = -4 if x ≠ 0
g(x) = 5 if x = 0
On the graph, when x is any value other than 0, the function takes the value of -4. This means that there will be a horizontal line at y = -4 for all x ≠ 0. The point (0, 5) will be represented by a solid dot since it's the only point where g(x) equals 5.
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What is the prime factorization of 140?
Answer: 2×2×5×7 or, in exponent form, [tex]2^2[/tex]×[tex]5^1[/tex]×[tex]7^1[/tex]
Step-by-step explanation:
We can use a factor tree to determine the prime factorization of 140. You may notice that there are several factors to choose from that will give us 140, but you can choose any because in the end it will give you the same answer!
140
14 × 10
2×7 2×5
That is all, because the final numbers listed are prime and we cannot perform any further actions.
Hope this helps!
The diagram shows a cuboid. 8 cm 15 cm 20 cm What is the volume of the cuboid?
Answer:
The answer is 2400 cm^3
Step-by-step explanation:
You just need to multiply the dimensions
Answer:
2400 cm³
Step-by-step explanation:
Volume of cuboid = length × width × height
Volume = 8 cm × 15 cm × 20 cm
Volume = 2400 cm³
So, the volume of the cuboid is 2400 cm³
Please write me a two column
The length of AB = CD and CD = AB based on the proof that :
Length AB is equal to length CDAB and CD are parallelLooking at the segments CD and AB, both segments are of equal length, hence they would be equal
Similarly , both segments are parallel and have the same end points. Hence, they are equal.
Therefore, AB = CD
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what is the volume of the cylinder below height 15 radius 11
Answer:
πr^2 h
π(11)^2 (15)
= 1815π or = 5701
Please help on question asap if you are correct with answer I'll give brainlie st, a thanks and five stars.
When we have a trapezium and w e are finding out the area , would it be possible to have a radius\diameter in the trapezium or is that just for 3D shapes
Is not possible to define a radius nor a diameter in a trapezium.
Is it possible to have a radius/diameter in the trapezium?Radius and diameter are two measures defined for circles.
Radius is the distance between the center and any point in the circumference, and the diameter is the distance between two opposite points in the circumference (so it does not need to be 3D to have radius/diameter).
At the same time, a trapezium is not a circle, is a quadrilateral, so it can't have any of these.
To get the area use the formula:
Area = (base1 + base2)*height / 2
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Which of the following gives the correct range for the piecewise graph?
A coordinate plane with a segment going from the point negative 3 comma 2 to 0 comma 1 and another segment going from the point 0 comma 1 to 5 comma negative 4.
The correct range for the piecewise graph is [-4, 2].
To solve this problemWe need to find the minimum and maximum values of the y-coordinates.
The first segment goes from (-3, 2) to (0, 1), so the range for this segment is from 1 to 2.
The second segment goes from (0, 1) to (5, -4), so the range for this segment is from -4 to 1.
We must take into account the minimum and maximum values from each segments in order to determine the overall range. The minimum and highest values are -4 and 2, respectively.
Therefore, the correct range for the piecewise graph is [-4, 2].
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Find prime factors of
48
So, the prime factors of 48 are 2 × 2 × 2 × 2 × 3 or we can also write them as 24 × 3, where 2 and 3 both are prime numbers.
Which of the following steps indicates the addition property of equality while solving the equation –1 – 6x = x – 15?
A) x = 14∕2
B) –1 – 6x = x – 15
C) 23 – 6x – 24 = x – 15
D) –1 – 6x + 15 = x – 15 + 15
Answer:
-1 - 6x = x - 15
Add 15 to both sides using the addition property of equality.
14 - 6x = x
14 = 7x
2 = x
D) -1 - 6x + 15 = x - 15 + 15
Answer and Step-by-step explanation:
Please refer to the photo for the solution!
7
9
S
.
3+
2-
D
A
3
4
Mark this and return
C
S
B
What is the area of parallelogram ABCD?
13 square units
O 14 square units
15 square units
16 square units
Save and Exit
Next
Submit
The area of the parallelogram ABCD is (a) 13 square units.
What is the area of the parallelogram?Area of a parallelogram = Length × Width
Length = distance AB
Where
A = (3, 6) and B = (6, 5)
So, we have
[tex]Length = \sqrt{ {(3 - 6)}^{2} + (6 - 5) ^{2} }[/tex]
[tex] = \sqrt{ {( - 3)}^{2} + (1) ^{2} }[/tex]
[tex] = \sqrt{ 9 + 1 }[/tex]
[tex]= \sqrt{10}[/tex]
Next, we have
Width = distance AD
Where
A = (3, 6) and D = (2, 2)
So, we have
[tex]width = \sqrt{ {(3 - 2)}^{2} + (6 - 2) ^{2} }[/tex]
[tex] = \sqrt{ {( 1)}^{2} + (4) ^{2} }[/tex]
[tex]= \sqrt{ 1 + 16 }[/tex]
[tex]= \sqrt{17}[/tex]
Recall that
Area of a parallelogram = Length × Width
So, we have
= √10 × √17
Evaluate the products
√170
Take the square rppt
= 13.03840481040529
Approximately, 13 square units
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Complete question:
What is the area of parallelogram ABCD?
O 13 square units
O 14 square units
O 15 square units
O 16 square units
See attachment
